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Coefficient[expr,form]

gives the coefficient of form in the polynomial expr.

Coefficient[expr,form,n]

gives the coefficient of form^n in expr.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Modulus  
Properties & Relations  
Possible Issues  
See Also
Tech Notes
Related Guides
Related Links
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Coefficient

Coefficient[expr,form]

gives the coefficient of form in the polynomial expr.

Coefficient[expr,form,n]

gives the coefficient of form^n in expr.

Details and Options

  • Coefficient picks only terms that contain the particular form specified. is not considered part of .
  • form can be a product of powers.
  • Coefficient[expr,form,0] picks out terms that are not proportional to form.
  • Coefficient works whether or not expr is explicitly given in expanded form.

Examples

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Basic Examples  (1)

Find coefficients of polynomials:

Wolfram Language code: Coefficient[(x + 1) ^ 3, x, 2]
Wolfram Language code: Coefficient[(x + y) ^ 4, x y ^ 3]

Scope  (4)

Find a coefficient at x:

Wolfram Language code: Coefficient[a x + b y + c, x]

Find a coefficient at a power of x:

Wolfram Language code: Coefficient[a x ^ 3 + b x ^ 2 + c x + d, x, 2]

Find the free term in a polynomial:

Wolfram Language code: Coefficient[(x + 2) ^ 2 + (x + 3) ^ 3, x, 0]

Find a coefficient at a multivariate monomial:

Wolfram Language code: Coefficient[(x + y)(x + 2y)(3x + 4y + 5), x y ^ 2]

Options  (1)

Modulus  (1)

Find a coefficient over the integers modulo 2:

Wolfram Language code: Coefficient[(x + 1) ^ 3, x, 2, Modulus -> 2]

Properties & Relations  (2)

CoefficientList gives a list of all polynomial coefficients:

Wolfram Language code: f = (x + 3) ^ 5;
Wolfram Language code: CoefficientList[f, x]

The same list of coefficients obtained using Coefficient and Exponent:

Wolfram Language code: Coefficient[f, x, #]& /@ Range[0, Exponent[f, x]]

For multivariate polynomials CoefficientList gives a tensor of the coefficients:

Wolfram Language code: f = (3x + 5y) ^ 4;
Wolfram Language code: cl = CoefficientList[f, {x, y}]

CoefficientArrays gives the list of arrays of polynomial coefficients ordered by total degree:

Wolfram Language code: ca = CoefficientArrays[f, {x, y}]

The coefficient of x y3:

Wolfram Language code: Coefficient[f, x y ^ 3]

In cl the coefficient of x^a y^b is the element at position {a+1,b+1}:

Wolfram Language code: cl[[1 + 1, 1 + 3]]

In ca the position of this coefficient is a+b+1 followed by a 1s and b 2s (1 and 2 indicate the first and second variables):

Wolfram Language code: ca[[5, 1, 2, 2, 2]]

Possible Issues  (1)

Coefficient treats transcendental powers as being algebraically unrelated to algebraic powers:

Wolfram Language code: Coefficient[x ^ s x, x ^ s]

Coefficient treats distinct transcendental powers as being algebraically unrelated to one another:

Wolfram Language code: Coefficient[x ^ s x ^ t, x ^ s]
Wolfram Research (1988), Coefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/Coefficient.html (updated 1996).

Text

Wolfram Research (1988), Coefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/Coefficient.html (updated 1996).

CMS

Wolfram Language. 1988. "Coefficient." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Coefficient.html.

APA

Wolfram Language. (1988). Coefficient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Coefficient.html

BibTeX

@misc{reference.wolfram_2026_coefficient, author="Wolfram Research", title="{Coefficient}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Coefficient.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_coefficient, organization={Wolfram Research}, title={Coefficient}, year={1996}, url={https://reference.wolfram.com/language/ref/Coefficient.html}, note=[Accessed: 13-June-2026]}